Another post about Les Paul circuitry customization: this time I’ll show the difference between the standard “modern” wiring and an alternate wiring I found here with “independent volume controls”.
The rationale about this mod is that with the standard wiring, when you set the 3-way switch on the middle position, if you turn fully down the volume of one pickup, you silence the signal of both. But how do this mod affect the controls behavior?

I’ll analyze here the circuit with only one pickup, i.e. with the 3-way switch NOT in the middle position.
The graph shown is a logarithmic plot of the frequency response between the pickup ideal signal and the output, for the two wirings, and for different positions of the volume potentiometer (I set ten values of a logarithmic sweep between 1 Ohm and 500 kOhm). The tone knob if fully on the bright position.

As you can see, with the alternate wiring, as soon as you turn the volume knob down the sound gets very very dark!
My bet is that this is not what you want, but if you want to try this mod anyway, go ahead and let your ears be the judge (I didn’t, I just run the simulation).

My opinion is that the volume silencing both pickups is a non-issue, actually, because if you need to silence just one pickup, why selecting both, anyway? You could just flip the 3-way switch and you’re done.

PS:
The software I used for the simulation is Qucs on Linux, but on the website you can find downloads for Windows and Mac OS X as well.
There’s no potentiometer component in Qucs, so I just used two resistors with the values bound together by the equation Rvb=500k-Rva.
For the pickup I chose values that, combining various sources, seem to be good representatives of a standard Gibson PAF pickup.